2021-03-02 08:32:40 +01:00
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
2021-04-14 08:03:54 +02:00
"## Uczenie maszynowe –
2021-03-02 08:32:40 +01:00
"# 13. Konwolucyjne sieci neuronowe"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Konwolucyjne sieci neuronowe wykorzystuje się do:\n",
"\n",
"* rozpoznawania obrazu\n",
"* analizy wideo\n",
"* innych zagadnień o podobnej strukturze"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Innymi słowy, CNN przydają się, gdy mamy bardzo dużo danych wejściowych, w których istotne jest ich sąsiedztwo."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Warstwy konwolucyjne"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Dla uproszczenia przyjmijmy, że mamy dane w postaci jendowymiarowej –
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Tak wygląda nasze nagranie:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" width=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv-9-xs.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"(ciąg próbek dźwiękowych –
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Najprostsza metoda –
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" width=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv-9-F.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Wady:\n",
"\n",
"* dużo danych wejściowych\n",
"* nie wykrywa własności „lokalnych” wejścia"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Chcielibyśmy wykrywać pewne lokalne „wzory” w danych wejściowych.\n",
"\n",
"W tym celu tworzymy mniejszą sieć neuronową (mniej neuronów wejściowych) i _kopiujemy_ ją tak, żeby każda jej kopia działała na pewnym fragmencie wejścia (fragmenty mogą nachodzić na siebie):"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img style=\"margin: auto\" width=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv-9-Conv2.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Każda z sieci A ma 2 neurony wejściowe (mało realistycznie). "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img style=\"margin: auto\" width=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv-9-Conv3.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Każda z sieci A ma 3 neurony wejściowe (wciąż mało realistycznie, ale już trochę bardziej). "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Warstwę sieci A nazywamy **warstwą konwolucyjną** (konwolucja = splot).\n",
"\n",
"Warstw konwolucyjnych może być więcej niż jedna:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv-9-Conv2Conv2.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"W dwóch wymiarach wygląda to tak:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv2-9x5-Conv2.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv2-9x5-Conv2Conv2.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Zblizenie na pojedynczą jednostkę A:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv2-unit.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Tak definiujemy formalnie funckję splotu dla 2 wymiarów:\n",
"\n",
"$$\n",
"\\left[\\begin{array}{ccc}\n",
"a & b & c\\\\\n",
"d & e & f\\\\\n",
"g & h & i\\\\\n",
"\\end{array}\\right]\n",
"*\n",
"\\left[\\begin{array}{ccc}\n",
"1 & 2 & 3\\\\\n",
"4 & 5 & 6\\\\\n",
"7 & 8 & 9\\\\\n",
"\\end{array}\\right] \n",
"=\\\\\n",
"(1 \\cdot a)+(2 \\cdot b)+(3 \\cdot c)+(4 \\cdot d)+(5 \\cdot e)\\\\+(6 \\cdot f)+(7 \\cdot g)+(8 \\cdot h)+(9 \\cdot i)\n",
"$$\n",
"\n",
"Więcej: https://en.wikipedia.org/wiki/Kernel_(image_processing)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"A tak to mniej więcej działa:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"https://devblogs.nvidia.com/wp-content/uploads/2015/11/Convolution_schematic.gif\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Jednostka warstwy konwolucyjnej może się składać z jednej lub kilku warstw neuronów:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv-A.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv-A-NIN.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Jeden neuron może odpowiadać np. za wykrywanie pionowych krawędzi, drugi poziomych, a jeszcze inny np. krzyżujących się linii."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Przykładowe filtry, których nauczyła się pierwsza warstwa konwolucyjna:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/KSH-filters.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### _Pooling_"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Obrazy składają się na ogół z milionów pikseli. Oznacza to, że nawet po zastosowaniu kilku warstw konwolucyjnych mielibyśmy sporo parametrów do wytrenowania.\n",
"\n",
"Żeby zredukować liczbę parametrów, a dzięki temu uprościć obliczenia, stosuje się warstwy **_pooling_**.\n",
"\n",
"_Pooling_ to rodzaj próbkowania. Najpopularniejszą jego odmianą jest _max-pooling_, czyli wybieranie najwyższej wartości spośród kilku sąsiadujących pikseli."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"https://upload.wikimedia.org/wikipedia/commons/e/e9/Max_pooling.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Warstwy _pooling_ i konwolucyjne można przeplatać ze sobą:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/Conv2-9x5-Conv2Max2Conv2.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"_Pooling_ –
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Do sieci konwolucujnych możemy dokładać też warstwy ReLU."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
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"text/html": [
"\n",
" <iframe\n",
" width=\"800\"\n",
" height=\"600\"\n",
" src=\"https://www.youtube.com/embed/FmpDIaiMIeA\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
],
"text/plain": [
"<IPython.lib.display.YouTubeVideo at 0x7f70ba22e910>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import IPython\n",
"IPython.display.YouTubeVideo('FmpDIaiMIeA', width=800, height=600)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Możliwości konwolucyjnych sieci neuronowych"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"<img style=\"margin: auto\" height=\"80%\" src=\"http://colah.github.io/posts/2014-07-Conv-Nets-Modular/img/KSH-results.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Przykład: MNIST"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"import math\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import random\n",
"\n",
"from IPython.display import YouTubeVideo"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# źródło: https://github.com/keras-team/keras/examples/minst_mlp.py\n",
"\n",
"import keras\n",
"from keras.datasets import mnist\n",
"\n",
"from keras.models import Sequential\n",
"from keras.layers import Dense, Dropout, Flatten\n",
"from keras.layers import Conv2D, MaxPooling2D\n",
"\n",
"# załaduj dane i podziel je na zbiory uczący i testowy\n",
"(x_train, y_train), (x_test, y_test) = mnist.load_data()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"def draw_examples(examples, captions=None):\n",
" plt.figure(figsize=(16, 4))\n",
" m = len(examples)\n",
" for i, example in enumerate(examples):\n",
" plt.subplot(100 + m * 10 + i + 1)\n",
" plt.imshow(example, cmap=plt.get_cmap('gray'))\n",
" plt.show()\n",
" if captions is not None:\n",
" print(6 * ' ' + (10 * ' ').join(str(captions[i]) for i in range(m)))"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x7f70ba2e9090>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" 5 0 4 1 9 2 1\n"
]
}
],
"source": [
"draw_examples(x_train[:7], captions=y_train)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"batch_size = 128\n",
"num_classes = 10\n",
"epochs = 12\n",
"\n",
"# input image dimensions\n",
"img_rows, img_cols = 28, 28"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"if keras.backend.image_data_format() == 'channels_first':\n",
" x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n",
" x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n",
" input_shape = (1, img_rows, img_cols)\n",
"else:\n",
" x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n",
" x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n",
" input_shape = (img_rows, img_cols, 1)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x_train shape: (60000, 28, 28, 1)\n",
"60000 train samples\n",
"10000 test samples\n"
]
}
],
"source": [
"x_train = x_train.astype('float32')\n",
"x_test = x_test.astype('float32')\n",
"x_train /= 255\n",
"x_test /= 255\n",
"print('x_train shape: {}'.format(x_train.shape))\n",
"print('{} train samples'.format(x_train.shape[0]))\n",
"print('{} test samples'.format(x_test.shape[0]))\n",
"\n",
"# convert class vectors to binary class matrices\n",
"y_train = keras.utils.to_categorical(y_train, num_classes)\n",
"y_test = keras.utils.to_categorical(y_test, num_classes)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"model = Sequential()\n",
"model.add(Conv2D(32, kernel_size=(3, 3),\n",
" activation='relu',\n",
" input_shape=input_shape))\n",
"model.add(Conv2D(64, (3, 3), activation='relu'))\n",
"model.add(MaxPooling2D(pool_size=(2, 2)))\n",
"model.add(Dropout(0.25))\n",
"model.add(Flatten())\n",
"model.add(Dense(128, activation='relu'))\n",
"model.add(Dropout(0.5))\n",
"model.add(Dense(num_classes, activation='softmax'))"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"model.compile(loss=keras.losses.categorical_crossentropy,\n",
" optimizer=keras.optimizers.Adadelta(),\n",
" metrics=['accuracy'])"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Train on 60000 samples, validate on 10000 samples\n",
"Epoch 1/12\n",
"60000/60000 [==============================] - 333s - loss: 0.3256 - acc: 0.9037 - val_loss: 0.0721 - val_acc: 0.9780\n",
"Epoch 2/12\n",
"60000/60000 [==============================] - 342s - loss: 0.1088 - acc: 0.9683 - val_loss: 0.0501 - val_acc: 0.9835\n",
"Epoch 3/12\n",
"60000/60000 [==============================] - 366s - loss: 0.0837 - acc: 0.9748 - val_loss: 0.0429 - val_acc: 0.9860\n",
"Epoch 4/12\n",
"60000/60000 [==============================] - 311s - loss: 0.0694 - acc: 0.9788 - val_loss: 0.0380 - val_acc: 0.9878\n",
"Epoch 5/12\n",
"60000/60000 [==============================] - 325s - loss: 0.0626 - acc: 0.9815 - val_loss: 0.0334 - val_acc: 0.9886\n",
"Epoch 6/12\n",
"60000/60000 [==============================] - 262s - loss: 0.0552 - acc: 0.9835 - val_loss: 0.0331 - val_acc: 0.9890\n",
"Epoch 7/12\n",
"60000/60000 [==============================] - 218s - loss: 0.0494 - acc: 0.9852 - val_loss: 0.0291 - val_acc: 0.9903\n",
"Epoch 8/12\n",
"60000/60000 [==============================] - 218s - loss: 0.0461 - acc: 0.9859 - val_loss: 0.0294 - val_acc: 0.9902\n",
"Epoch 9/12\n",
"60000/60000 [==============================] - 219s - loss: 0.0423 - acc: 0.9869 - val_loss: 0.0287 - val_acc: 0.9907\n",
"Epoch 10/12\n",
"60000/60000 [==============================] - 218s - loss: 0.0418 - acc: 0.9875 - val_loss: 0.0299 - val_acc: 0.9906\n",
"Epoch 11/12\n",
"60000/60000 [==============================] - 218s - loss: 0.0388 - acc: 0.9879 - val_loss: 0.0304 - val_acc: 0.9905\n",
"Epoch 12/12\n",
"60000/60000 [==============================] - 218s - loss: 0.0366 - acc: 0.9889 - val_loss: 0.0275 - val_acc: 0.9910\n"
]
},
{
"data": {
"text/plain": [
"<keras.callbacks.History at 0x7f70b80b1a10>"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.fit(x_train, y_train,\n",
" batch_size=batch_size,\n",
" epochs=epochs,\n",
" verbose=1,\n",
" validation_data=(x_test, y_test))"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Test loss:', 0.027530849870144449)\n",
"('Test accuracy:', 0.99099999999999999)\n"
]
}
],
"source": [
"score = model.evaluate(x_test, y_test, verbose=0)\n",
"print('Test loss:', score[0])\n",
"print('Test accuracy:', score[1])"
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
},
"livereveal": {
"start_slideshow_at": "selected",
2021-04-14 08:03:54 +02:00
"theme": "white"
2021-03-02 08:32:40 +01:00
}
},
"nbformat": 4,
"nbformat_minor": 4
}
